`USCA = ((1+i%)^n-1)/(i%) `

Enter a value for all fields

The  Uniform Series Compound Amount (USCA)calculator computes USCA based on the number of periods and the interest rate per period.

INSTRUCTIONS:  Choose units and enter the following:

• (i) Interest Rate per Period
• (n) Number of periods

Uniform Series Compund Amount factor (USCA):  The calculator returns the factor.

The Math / Science

The formula for the Uniform Series Compound Amount (USCA) factor is:

  `USCA= ( (1+i)^n -1)/i`

where:

• UGUS is the uniform gradient uniform series factor.
• i is the interest rate per period
• n is the number of periods.

This equation solves for the Uniform Series Compound Amount factor (USCAF), a Discrete Compounding Discount Factor.  This factor is used to determine the future sum (F) of a known uniform annual series with uniform amount ‘A'.

This factor is multiplied with an annualized investment amount to calculate the Future Value of a principle amount invested now in an account that provides a compounded interest growth.

EXAMPLES

The USCA factor is used to answer questions of the form:

If I invest $100 monthly in an account that provides 5% interest, what will be the Future Value of the investment in 5 years?

This is answered by inputting:

• n = 5 
• i% = 5

The Future Value of $100 investments FV = USCA (5%,5 yrs] * investment ($100) = 5.52563125 * $100 =   $552.56

When you make a series of fixed payments over a period of time - such as rent or car payments - or receive a series of payments over a period of time, such as bond coupons. These are called annuities. Annuities are basically a series of payments (fixed amount) paid to you or by you at a specific defined recurring frequency over the course of a fixed amount of time. These payments can be made: yearly, semi-annually (twice a year), quarterly, or monthly.

In one form of Annuity; payments are made at the end of the period. For example, bonds usually distribute coupon payments each six months until the bond's maturity date.  In another form of annuity, the Annuity Due type of account; payments are made at the beginning of each period. Rent is an example of annuity due. You are usually required to pay rent at the beginning of the month, and then on each subsequent month thereafter.  This is an Annuity due from the renter.

Using the Annuity concept for investment, if you can invest a certain dollar amount on a regular interval for a certain time period, the USCA discount factor can be used to find out how much your investment would be worth in the future (using the interest rate and number of periods).

REFERENCE

• Lindeburg, Michael R (1992). Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.